BiP clustering facilitates protein folding in the endoplasmic reticulum

BiP Clustering Facilitates Protein Folding in theEndoplasmic ReticulumMarc Griesemer1.*, Carissa Young2., Anne S. Robinson2,3, Linda Petzold4

1 Department of Applied Mathematics, University of California, Merced, Merced, California, United States of America, 2 Department of Chemical Engineering, University of

Delaware, Newark, Delaware, United States of America, 3 Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana, United States

of America, 4 Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America

Abstract

The chaperone BiP participates in several regulatory processes within the endoplasmic reticulum (ER): translocation, proteinfolding, and ER-associated degradation. To facilitate protein folding, a cooperative mechanism known as entropic pullinghas been proposed to demonstrate the molecular-level understanding of how multiple BiP molecules bind to nascent andunfolded proteins. Recently, experimental evidence revealed the spatial heterogeneity of BiP within the nuclear andperipheral ER of S. cerevisiae (commonly referred to as ‘clusters’). Here, we developed a model to evaluate the potentialadvantages of accounting for multiple BiP molecules binding to peptides, while proposing that BiP’s spatial heterogeneitymay enhance protein folding and maturation. Scenarios were simulated to gauge the effectiveness of binding multiplechaperone molecules to peptides. Using two metrics: folding efficiency and chaperone cost, we determined that the singlebinding site model achieves a higher efficiency than models characterized by multiple binding sites, in the absence ofcooperativity. Due to entropic pulling, however, multiple chaperones perform in concert to facilitate the resolubilization andultimate yield of folded proteins. As a result of cooperativity, multiple binding site models used fewer BiP molecules andmaintained a higher folding efficiency than the single binding site model. These insilico investigations reveal that clusters ofBiP molecules bound to unfolded proteins may enhance folding efficiency through cooperative action via entropic pulling.

Citation: Griesemer M, Young C, Robinson AS, Petzold L (2014) BiP Clustering Facilitates Protein Folding in the Endoplasmic Reticulum. PLoS Comput Biol 10(7):e1003675. doi:10.1371/journal.pcbi.1003675

Editor: James M. Briggs, University of Houston, United States of America

Received November 4, 2013; Accepted May 3, 2014; Published July 3, 2014

Copyright: � 2014 Griesemer et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: Funding provided by the NSF Integrative Graduate Education and Research Traineeship (IGERT) 0221651 (CY) and 0221715 (MG) and by the NationalInstitute of Health under grant R01 GM75297. This publication was made possible with the support of P20RR015588 under the COBRE program of the NationalCenter for Research Resources (NCRR) at the NIH (to ASR). The funders had no role in study design, data collection and analysis, decision to publish, or preparationof the manuscript.

Competing Interests: The authors have declared that no competing interests exist.

* Email: [email protected]

. These authors contributed equally to this work.

Introduction

Protein homeostasis, or proteostasis, is characterized by the

integration of biological pathways that modulate protein biogen-

esis, maturation, transport, and degradation. As a critical element

to cell survival, networks of molecular chaperones, foldases, and

quality control components minimize the effects of cell stress in

order to revert to a homeostatic environment [1]. Proteostasis

occurs in distinct subcellular environments and is constantly

monitored by stress-signaling pathways. In eukaryotes, the

endoplasmic reticulum (ER) is the first membrane-enclosed

organelle of the secretory pathway, which ascertains the fidelity

of protein folding, maturation, biogenesis (i.e. translation and ER

translocation), and ER-associated degradation (ERAD). In the

yeast S. cerevisiae, multiple ER quality control mechanisms have

been identified to modulate these critical ER processes, including

associated chaperone/co-chaperone interactions. Specifically,

molecular chaperones dissociate aggregates, self-associating con-

glomerations of unfolded and misfolded proteins, which would

otherwise interfere with the cell homeostasis leading to cell

dysfunction and death [2]. Despite the ubiquitous nature of

molecular chaperones, a variety of insults can overwhelm the ER’s

processing capacity including nutrient deprivation, pathogenic

infection, cell differentiation, or alterations in calcium concentra-

tion or redox status. As a consequence of ER stress, aberrant

proteins accumulate within this organelle, triggering intracellular

pathways collectively referred to as the unfolded protein response

(UPR). In eukaryotes, the UPR transcriptionally up-regulates

genes encoding molecular chaperones [3], ERAD machinery [4–

7], key enzymes of lipid biosynthesis [8], and other components of

the secretory pathway [9–11]. Notably, several key features of the

UPR are conserved across eukaryotes; although expanded in

scope, the mammalian UPR has similar attributes to that of S.

cerevisiae, particularly with respect to the Ire1p-dependent regula-

tion of unfolded proteins and BiP modulation of the response

(reviewed [12]). The elucidation of these pathways – specifically

the interplay between UPR and ERAD – has become of growing

importance in therapeutics as loss of proteostasis has been

suggested to lead to a number of human diseases including

Alzheimer’s, Parkinson’s Disease and Type II Diabetes [13].

In the early secretory pathway, protein fidelity is attributed to

select chaperone/co-chaperone interactions (Hsp70 and Hsp40

proteins, respectively) conserved via evolution from yeast to

humans. As one of two distinct Hsp70 molecular chaperones in the

ER, BiP/Kar2p binds preferentially to hydrophobic residues of

nascent or unfolded proteins [14,15]. BiP, the yeast homolog of

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binding protein immunoglobulin (referred to as Kar2/Grp78

[16]), has been identified as an essential component of ER

translocation, protein folding and maturation, karyogamy, and

ERAD [17–20]. To facilitate protein folding, co-chaperones

stimulate the binding of BiP to substrates whereas nucleotide

exchange factors (NEFs) assist in BiP’s stochastic release via cycles

dependent upon adenosine triphosphate (ATP). For example, co-

chaperone Sec63 directly interacts with BiP, increasing its affinity

for nascent proteins as they advance through the translocation

pore in S. cerevisiae [21–23]. In yeast, the posttranslational

translocation of nascent peptides is mediated by a heptameric

Sec complex, composed of Sec63, Sec62, as well as the

heterotrimer Sec61, which serves as the protein-conducting

channel [24,25]. Photo-cross-linking experiments have shown that

nascent peptides are in continuous contact with Sec61 during

protein translocation [26]. More recently, cryo-electron micros-

copy established that a single Sec61 heterotrimer enables the

progress of nascent proteins across the ER membrane, a conserved

feature manifested in both yeast and mammals [27]. In addition to

ER translocation, BiP’s interaction with co-chaperone Scj1 has

been implicated in protein folding and maturation [28,29], and

degradation of aberrant proteins [30].

ER translocation, protein folding and maturation, as well as

ERAD are conserved mechanisms across eukaryotes. As such, the

model eukaryotic organism, S. cerevisiae, provides an effective

experimental platform to elucidate an improved mechanistic-

understanding of proteostasis, specifically with regards to ER

chaperone/co-chaperone interactions. Proteomic studies have

identified absolute levels of protein expression and verified the

location of ER-resident proteins [31,32]. These data suggest that

the ER-resident chaperone BiP exceeds the level of all co-

chaperones in the ER by at least an order of magnitude at

conditions of normal growth, and is significantly up-regulated

during the UPR [6,33] indicating a significant increase in BiP’s

total abundance. Furthermore, BiP binds to substrates with

varying affinities [14], suggesting BiP responds to the protein’s

folding requirements. Interestingly, from an experimental per-

spective, the spatial localization of ER-resident chaperones or co-

chaperones has been evaluated for only Sec63 during the process

of translocation. In yeast, membrane protein Sec63 must by

necessity be localized at the ER membrane in order for nascent

proteins to translocate [34]. Collectively, this evidence suggests

that BiP’s spatiotemporal profile may be a contributing factor to its

diversity and functionality in the ER. This hypothesis was

Author Summary

The misfolding of proteins carries important implicationsfor diseases such as Alzheimer’s, Parkinson’s, cancer, anddiabetes. Once misfolded, proteins tend to associate intoaggregates that pose a toxic threat to the cell. Chaperonesare proteins that rescue the cell from an accumulation ofthese maladjusted proteins through dissociation of toxicoligomers and proper (re)folding. The endoplasmic retic-ulum (ER) is an organelle that serves as the staging groundfor the chaperone activities of protein transport, folding,and maturation in the early secretory pathway. We havedeveloped a computational model to investigate potentialmechanisms that enable multiple ER-resident moleculesworking in concert to effectively fold peptides andtransport nascent proteins across the ER membrane.Although previous models focused on chaperone interac-tions with peptides, we have explored the influence ofcooperativity among chaperone molecules to assist inprotein folding and maturation. We found that chaperonecooperation led to a higher yield of folded moleculescompared to when chaperones bound to peptides in a 1:1stoichiometry. We have concluded that the clustering ormultiple binding of chaperones may facilitate proteinfolding in vivo.

Figure 1. Models defined by number of binding sites. Schematic of the 4 models defined by the number of binding sites.doi:10.1371/journal.pcbi.1003675.g001

BiP Clustering Facilitates Protein Folding


previously posited and computationally explored [35]. Those

results were in agreement with Sec63 experimental results, and

further suggested that BiP clusters may exist in order to facilitate

the efficient translocation of nascent proteins.

That BiP performs disparate functions owes to its tendency to

bind many different types of proteins. Binding of multiple

chaperones to unfolded proteins has been established and

determined to be kinetically favorable [36]. The transport of

nascent proteins into the ER involves many BiP molecules working

in concert. Algorithms to predict binding sites have been

developed, and there are many examples of proteins that have

repeated hydrophobic stretches of amino acids [15,37,38], which

predict the presence of multiple binding sites. Aggregates have also

been found to have the analogous binding sites [39], while their

large size implies that multiple BiP molecules could engage them

at individual sites simultaneously. Here, we refer to clustering as

the process by which multiple BiP molecules bind to individual

binding sites that can be predicted from hydrophobic residues

along the length of the protein. This is in contrast to aggregation,

where self-associating conglomerations of unfolded and misfolded

proteins combine into larger toxic structures.

Experimental evidence has revealed that the refolding of

misfolded proteins and aggregates occurs in the presence of a

molar excess of chaperones [40], which led investigators to

propose that multiple chaperones apply a cooperative stretching

force known as entropic pulling [41,42]. The random motion of

several bound individual chaperones on a peptide can sum up to

an effective unfolding enabling re-initialization of the folding

process. The additional molecules provide an inertial brace that

stabilizes the interaction between chaperone and protein. In the

case of chaperone-mediated disaggregation, the brace is the

aggregate itself. A similar mechanism enables chaperones to assist

nascent peptides during ER translocation.

Cooperative action underlies many cellular processes including

signal transduction [43], protein transport [44], and chemotaxis

[45]. In the chaperone system, binding is not cooperatively

enhanced. Rather, the rate of solubilization and renaturing of

proteins increases with the number of chaperone molecules [40].

In this study, we created a computational model to investigate

the extent that an ER-resident chaperone, BiP — spatially

localized to ‘‘clusters’’ — may influence the extent of protein

folding. Our model includes BiP, the co-chaperones Scj1 and

Figure 2. Schematic of the processes in the ER and their spatial location. Protein translocation occurs at the ER membrane, while the otherprocesses can occur in the ER lumen. Processes include: (a) translocation; (b) folding/unfolding/misfolding; (c) aggregation; (d) disaggregation; (e)sequestration. Species are represented as follows: nascent protein (N); folded protein (F); unfolded protein (U); misfolded protein (M); BiP;Translocation Pore (Sec61); Sec63; size 2 aggregate (A2); size 3 aggregate (A3); size 4 aggregate (A4).doi:10.1371/journal.pcbi.1003675.g002



Sec63, and multiple states corresponding to unfolded proteins and

complexes. This work implements ER-resident chaperone/co-

chaperone interactions, experimental insights [21,46–48], esti-

mates of species concentrations determined for S. cerevisiae [32],

and binding affinities between BiP, Sec63, and synthetic peptides

[46,47]. When experimental data were not available, established

estimates from the mammalian literature for these highly

conserved mechanisms and proteins were used (Text S1, Table

S1, Supporting Information). To assess the potential advantages of

clusters, this model was used to evaluate the extent to which

gradients of BiP molecules may facilitate its activities in protein

folding and aggregate disassembly. Previous models [49–59] have

included varying aspects of chaperone activities and interactions,

yet only accounted for a single binding site scenario; in contrast,

our model focuses on multiple binding as the mechanism to

facilitate BiP’s roles in the ER.

This study provides a detailed analysis of (i) the quantitative

impact of chaperone clustering activity in the ER and contributing

factors leading to efficient protein folding; and (ii) the potential

mechanisms and interplay among components of ER quality

control. Together, this framework provides an improved mecha-

nistic understanding of chaperone/co-chaperone interactions, as

well as possible strategies to minimize the accumulation of

misfolded proteins.

Models

Model DescriptionWe created an ordinary differential equation (ODE) model to

study the efficiency of protein folding due to the molecular

heterogeneity of ER-resident chaperone, BiP. Four sub-models

were created that differ by the stoichiometry of binding sites to

the protein species: one, two, three, and four (as shown in

Figure 1). To evaluate model performance two metrics were

accounted for: (i) folding efficiency (i.e., fraction of proteins

folded); and (ii) chaperone cost (e.g., the molecular resources

needed to achieve a specified level of efficiency). A schematic of

the ER, as well as prominent protein-protein interactions, is

shown in Figure 2. A total of 60 species and 125 reactions are

evident in the largest model. Within a model, numerous states

have been depicted in Figure 3. A comprehensive list of all

reactions, states, rates and initial conditions is referenced in the

Figure 3. Schematic of the ODE model. Background colors represent translocation (orange), unfolding (green), misfolding (yellow), andaggregation/disaggregation (red) modules. Additional states and reactions involving the luminal co-chaperone Scj1 are accounted for in theaggregation, unfolded, and misfolded modules, but are omitted from this diagram due to space limitations. Species are represented as follows: Pore;nascent protein (N), sliding state (x); folded protein (F); unfolded protein (U); misfolded protein (M); BiP; Sec63; size 2 aggregate (A2); size 3 aggregate(A3); size 4 aggregate (A4). Sliding states (x) mimic the movement of the nascent protein further into the lumen.doi:10.1371/journal.pcbi.1003675.g003



Supporting Information. The initial units of species abundance

were converted to concentration by incorporating an ER volume

of 0.7 mm3 [60]. Model parameters were obtained from literature

sources (where available), as detailed in the Supporting Informa-

tion (Text S1, Tables S1–S7).

Model StructureOur model monitored the fate of soluble proteins within the ER

lumen by investigating the composition of six modules, as follows:

1. Protein Synthesis and Translocation

A nascent protein (N) is synthesized by a ribosome localized on

the ER membrane (cytosolic interface) near the translocon, as

shown in Figure 2a. Sec61 channels, referred to as transloca-

tion pores, are activated by the binding of co-chaperone Sec63,

and nascent proteins can then start the process of translocation

through the ER membrane. In this study, we modeled the

movement of nascent proteins across the ER membrane as

post-translational translocation, which directly involves the Sec

complex of eukaryotes. The nascent protein progresses forward

into the pore channel (Pore-Sec63-NRPore-Sec63-Nx), expos-

ing a binding site (x) within the lumen where a BiP molecule

may bind. We assume that a BiP molecule preferentially binds

at a site closest to the membrane, consisting of hydrophobic

residues, as the co-chaperone/chaperone interaction facilitates

this binding (Pore-Sec63-Nx+BiPRPore-Sec63-N-BiP). Subse-

quently, a nascent protein can irreversibly proceed into the

lumen, thus exposing a second binding site to BiP at the

channel; however, it cannot assume the first configuration that

consisted of the initial BiP at the membrane, since BiP acts as a

‘‘stopper’’ to prevent this motion. This cycle continues until the

nascent protein has completely exited the channel. The nascent

Figure 4. Folding efficiency vs. BiP binding rate without cooperativity. Comparison of the folding efficiency (i.e. fraction of proteins folded)as a function of the binding rate between BiP and unfolded proteins. In this scenario, there is no cooperative effect among chaperones in folding,unfolding, or disaggregating proteins. The model number refers to the number of binding sites. In this scenario, Model 1 has the highest foldingefficiency, followed by Models 2, 3 and 4.doi:10.1371/journal.pcbi.1003675.g004



protein then dissociates from the Pore-Sec63 complex and is

now classified as an unfolded protein (U), with bound BiP

molecules spaced intermittently along the length of the peptide.

In this model, the Pore-Sec63 complex disassociates into its

constituent proteins, yet whether Sec61 pores are involved in

successive rounds of ER translocation is unclear [61–63].

2. Misfolding, Unfolding, and Productive Folding

This multifaceted pathway is detailed in Figure 2b. In this

scenario, the default initial protein state is unfolded, but may

terminally misfold, a circumstance dependent on the ratio of

unfolded proteins to chaperones. Misfolded proteins cannot

spontaneously progress towards an unfolded state since a key

role of chaperone/co-chaperone systems is to bind to

misfolded proteins and unfold them, thereby resulting in an

opportunity to fold to its proper confirmation. In this model,

the mechanism of the chaperone system begins with

unfolded or misfolded proteins binding to the J-type co-

chaperone Scj1 (analogous to Erj3 in humans) or with BiP

forming binary complexes (Scj1:U/M or BiP:U/M, where

the ‘‘/’’ indicates ‘‘either-or’’). BiP binds weakly to substrates

while Scj1 accelerates ATP hydrolysis to facilitate BiP’s

conformational change, thus an increased affinity between

BiP and the unfolded protein. Consequently, BiP and Scj1

may act synergistically. BiP molecules bound to U/M

passively prevent misfolding and aggregation (or in the case

of aggregates, further oligomerization). Unfolded proteins

fold either spontaneously or by chaperone assistance [64–67].

3. Aggregation

Aggregation is illustrated in Figure 2c. Our model describes

aggregation as a process in which non-native proteins associate

and evolve by the addition of unfolded or misfolded proteins.

Aggregation by this process could lead to large masses of

hundreds of monomers, which as a model would be intractable

computationally. Thus, we limited the size of aggregates to

four. Notably, larger aggregates require the assistance of

additional ERQC components other than BiP and Scj1 alone

[68], limiting applicability here. Each aggregate maintains a

number of binding sites up to the size of the aggregate and/or

the number of binding sites of the model, whichever is less.

Thus, the single binding site model has only one binding site

even for a size four aggregate (A4), while the four site model

has four binding sites on A4. The rate of accumulation of

proteins into aggregates is assumed to be equal for all sizes of

aggregates (107 M21 s21), except the first step (nucleation)

which was constrained as one-tenth of all sequential steps, thus

rate-limiting [69]. We assume that the aggregation is

irreversible except through the action of chaperones. To

substantiate this assumption, Diamant et al. [68] demonstrated

that Hsp70 chaperones have a diminished ability to re-

solubilize very large aggregates by themselves.

Figure 5. Relative protein coverage. Protein coverage of the four models relative to Model 1 in the noncooperative scenario. Coverage refers tothe percentage of proteins that are protected from misfolded and aggregation at any one time.doi:10.1371/journal.pcbi.1003675.g005



4. Disaggregation

Disaggregation is shown in Figure 2d. Disaggregation is critical for

the recovery of ER homeostasis following the accumulation of

protein aggregates due to classical cell stress responses, such the

heat shock response or UPR. Successful disaggregation leads to a

misfolded monomer bound to a single chaperone, while the

remaining chaperones and aggregate exist in a complex [Aj-1-iBiP

where j-1 is the new aggregate size and i is the number of BiPs still

bound to the aggregate. We have assumed that aggregates do not

dissociate freely, in the absence of chaperone interactions [70,71].

However, chaperones can extract a constituent misfolded protein

from the aggregate, reducing the aggregate size. In an iterative

manner, this process yields total disaggregation. Scj1 facilitates

BiP’s function by binding initially to the aggregate before ATP

hydrolysis, thus securing the ER-resident chaperone, BiP, to the

substrate [72]. Chaperone/co-chaperone interactions stabilize the

aggregate at its current size. As with the folding or triage reactions,

BiP can perform disaggregation independent of Scj1, but at a

lower binding rate. We set the disaggregation rate to 1 s21 for

BiP-only mediated reactions.

5. Sequestration

Aggregates can become insoluble, inert bodies (I). We assumed

a single rate of irreversible entrapment for all aggregated

species. Chaperones are lost, as they become entangled in these

structures and eventually degrade by ERAD. We set this

insoluble rate to 1 s21 [59]. Figure 2e illustrates this process.

Cooperativity. Cooperativity is modeled as entropic pulling,

via mass-action reactions, and highlighted in the example reactions

below (see Tables S2–S7 in Text S1 for the full description),

U-2BiP?Fz2BiP ð1Þ

M-2BiP?U-2BiP ð2Þ

A2-2BiP?M-BiPzM-BiP: ð3Þ

Model Metric EquationsIn this study we assessed two model metrics: folding efficiency and

chaperone cost. The former is given by the total number of folded

proteins at the end of the simulation divided by the total number of

unfolded proteins (yielding a fractional range between zero and one),

Figure 6. Protein coverage. Time series of the amount of bound protein for the different models, showing greater coverage for the single bindingsite model.doi:10.1371/journal.pcbi.1003675.g006



FE~F

Utotal

: ð4Þ

Chaperone cost is defined as the average number of bound

chaperones per unfolded protein per unit time. This metric combines

the time spent on the protein with the total number of chaperones

bound at the end of the simulation,

CC~BiPbound

dt: ð5Þ

Results

Model ResultsSteady-state solutions for the four model cases (corresponding to

1, 2, 3 or 4 binding sites) were completed for different values of BiP

association to unfolded proteins. Figure 4 compares the models in

terms of folding efficiency (i.e., total folded as a percentage of total

protein) and association rate. In the absence of cooperativity, the

single binding site model (Model 1) yields increased levels of folded

protein, as unfolded protein binding sites are more easily

saturated, providing more BiP coverage of the unfolded protein

population (Figure 5). When one examines the time of interaction

between BiP and unfolded proteins, BiP covers more proteins,

each for a longer period of time (in protein per second) as

compared to the alternative models (Figure 6). This effect occurs at

low ratios of BiP:U, hence the chaperone is classified as a ‘holdase’

[73]. However, the simpler non-cooperative models are incom-

plete in describing the entropic pulling data [40], hinting that

multiple BiPs must also act as a cooperative ‘unfoldase’, in line

with previous observations [73].

In comparison to other models herein, the degree of folding in

the single binding site model is more highly dependent on the

Figure 7. Folding efficiency vs. BiP binding rate with cooperativity. Comparison of the folding efficiency (i.e. fraction of proteins folded) as a functionof the binding rate between BiP and unfolded proteins with a cooperativity factor of C = 10. In this scenario, Model 2 has the highest folding efficiency.doi:10.1371/journal.pcbi.1003675.g007



association rate (Figure 4). Multiple BiP binding events minimize

the potential of an unfolded protein towards either misfolding or

aggregation pathways, as a consequence of redundant binding

events. We have not accounted for ATP molecules in our

simulations, since this aspect would only be of concern in a

depleted ATP environment [70].

In line with the entropic pulling contributing to BiP function, we

increased the rates of folding, unfolding, and disaggregation by a

factor of C, to reflect the cooperativity of multiple chaperones

participating in these select intracellular activities. With C = 10

(e.g., the lower end of the range (1–100) reported in the literature

[41], Model 2 resulted in the highest level of folded protein. Less

folding was observed in Models 3 and 4 as compared to Model 2

since coverage competes with cooperativity (Figure 7). When

cooperativity is implemented, the folding efficiency for Models 2,

3, and 4 increases; Model 2 performs optimally for C.5, as shown

in Figure 8.

We then varied the concentrations of total BiP and unfolded

protein to examine the effect on the two metrics described

previously. As expected, increased concentrations of BiP led to

higher levels of folding and less aggregation. Unexpectedly, we

discovered that the ratio of BiP:U is a more important factor than

the concentrations of either species alone. In the noncooperative

scenario, Model 1 produced the most folding (Figure 9); however,

when cooperativity was added, Models 2–4 attained higher folding

efficiencies (Figure 10). These results suggest that when the BiP:U

ratio is low (e.g., conditions of ER stress), cooperativity provides an

advantage for multiple binding. At higher BiP concentrations (i.e.,

relative to the concentration of U), cooperativity became a factor

of less importance since the majority of unfolded proteins were

protected from aggregation. As a result, more binding sites were

occupied, leading to an equalization in the total amount of folding

among the four models, i.e. the cooperativity effect was less

pronounced.

Figure 11 shows that chaperone cost (i.e., average chaperones

bound per second compared to unfolded, misfolded and aggre-

gated proteins) decreased substantially for Models 2, 3 and 4 in

comparison with Model 1, as shown for the cooperative case. In

general, it is better to maintain a lower cost metric resulting in

fewer chaperones bound per second. Due to the faster rates of

disaggregation, unfolding, and folding in the cooperative scenario

for Models 2, 3 and 4, chaperones maintained a shorter

interaction with proteins. More chaperones were engaged with a

single protein in Models 2–4, yet this result was counteracted by

decreased time that chaperones were bound to the protein.

Parameter Correlation StudyTo investigate the correlation between parameters and folding

efficiency for the different models and cooperativity scenarios, a

heatmap is shown in Figure 12. In this study, we varied BiP’s

Figure 8. Folding efficiency vs. cooperativity. Folding efficiency of the four models as a function of the cooperativity factor.doi:10.1371/journal.pcbi.1003675.g008



association rate, the aggregation rate from 103 to 108 M21 s21

and varied the folding, unfolding, misfolding, BiP disassociation,

and sequestering rates from 102 to 1023 s. Over these six orders of

magnitude, the folding efficiencies were recorded then correlations

were completed between parameter ranges and folding efficien-

cies. Note: this analysis varied one parameter at a time, while

keeping the others constant.

1. The BiP-U association rate has a positive correlation with the

folding efficiency of 0.5–0.6 for all models and cooperativities.

Thus, although the folding efficiencies are different for the four

models and cooperativity scenarios, the increases in efficiency

are proportional to each other. The recruitment of BiP to

proteins is also enhanced by the co-chaperone Scj1 interac-

tions. The medium correlation most likely occurs as a

consequence of minimal BiP molecules bound to a fraction of

unfolded proteins, i.e. the coverage effect.

2. The BiP-U disassociation rate is highly anti-correlated with

the folding efficiency (,20.99). When the disassociation

rate is low, BiP remains bound to the protein (or aggregate),

thus allowing for additional time for triage and ultimately

folding.

3. The aggregation rate is negatively correlated with the folding

efficiency for all models and scenarios. This effect is directly

dependent upon folding and aggregation, processes that are in

kinetic competition.

4. For the non-cooperative scenario, the unfolding rate is

uncorrelated with the folding efficiency across six orders of

magnitude. In contrast, chaperones increasingly impact

unfolding and maintain a positive correlation with respect to

folding yield, within the cooperative scenarios. Since chaper-

ones are involved, the BIP-U association and disassociation

rates influence the yield to a greater extent, with the

cooperativity factor tipping the balance towards higher levels

of folding.

5. The misfolding rate is uncorrelated with all folding efficiencies

across models and cooperativity scenarios equal in folding

yield. We hypothesized that these results are due to the

presence of chaperones on unfolded proteins that prevent

misfolding; similarly, misfolded proteins that are extracted from

aggregates are stabilized by a chaperone.

6. The folding rate is correlated positively with increasing folding

efficiency, although the correlation is not 1.

Figure 9. Folding efficiency vs. number of BiP molecules. Comparison of the folding efficiency as a function of the number of BiP moleculeswith no cooperativity and U = 1.0 ? 106 molecules. In this scenario, Model 1 folds most efficiently.doi:10.1371/journal.pcbi.1003675.g009



7. The sequestration rate is correlated negatively with folding

efficiency. This result is due to two effects: (i) the loss of proteins

into these insoluble structures that are not available for folding;

and (ii) the entrapment of chaperones that results in lower BiP

concentrations, which also has a negative effect on folding

yields.

In addition to the single parameter study, we performed a

variance-based global sensitivity analysis, in which we varied

seven parameters (the BiP association rate, the BiP disassociation

rate, the aggregation rate, the unfolding rate, the misfolding rate,

the folding rate, and the sequestration rate) over two orders of

magnitude simultaneously, and produced 100,000 parameter sets

as input to the seven models (four non-cooperative and three

cooperative models). We ran each simulation to steady state and

recorded the metrics of folding efficiency and chaperone cost.

From the variance-based global sensitivity analysis we learned

that the sequestration rate and the aggregation rate were the

dominant contributors to the variance of the output. However the

variance was quite small. Our graphs then revealed for all seven

parameters that the output mean across regions of parameter

space was essentially constant within a model. This remarkable

result indicates that the model output is rather invariant to

changes in parameters. Instead our results show that model

structure (the number of binding sites) and the cooperativity

factor play a critical role in the behavior of the models. In

addition, we also varied the concentrations of BiP and unfolded

protein (U). All of these results are in Text S2, the Global

Sensitivity Analysis Supplement.

TranslocationFinally, a translocation scenario was implemented to evaluate

the impact of BiP clustering in a dynamic environment. In five

different scenarios, a protein flux of 10, 100, 1000, 10000, and

100000 molecules per second was added to the ER [74] over a

period of 100 seconds. Thus, many more molecules transverse the

membrane to enter the ER lumen, with 106 molecules initially

localized in the lumen as in the steady-state case. This approach

was used to mimic general ER stress in yeast. We determined that

the translocation flux is highly negatively correlated (20.96 to 2

0.99) with folding efficiency (Figure 13). This result was expected;

as the protein flux increases, nascent proteins accumulate at the

cytosol/ER membrane interface due to the limited number of pore

complexes while BiP preferentially localized to ER the membrane

as compared to the lumen. In the non-cooperative model, Model 1

has the highest efficiency due to the coverage effect. When

cooperativity is accounted for, the multiple binding models yield a

higher folding efficiency. If no unfolded proteins exist in the

Figure 10. Folding efficiency vs. number of BiP molecules, cooperative scenario. Folding efficiency of the four models as a function of BiPconcentration with cooperativity factor C = 10. In this scenario, Model 2 folds most efficiently.doi:10.1371/journal.pcbi.1003675.g010



lumen, initially most proteins are protected and the folding

efficiency is close to 1 (simulation data not shown).

Discussion

The chaperone BiP participates in many critical ER processes,

including translocation, protein folding, disaggregation, and

degradation. To elucidate an improved mechanistic understanding

of ER proteostasis, we constructed a computational model to

evaluate ER-resident chaperone/co-chaperone interactions in

which multiple BiP molecules interact with nascent and unfolded

proteins to facilitate protein folding and maturation. In contrast to

established models that focused only on a single site for chaperone

binding events, we modeled the mechanism of entropic pulling, in

which several chaperones operate in concert to unfold and

disaggregate peptides by incorporating a stretching force caused

by random motions of the individual chaperones. In order to

investigate the acceleration of nascent proteins across an organelle

membrane, entropic pulling unifies aspects of both the Brownian

ratchet model [61] and power stroke model [75,76] exceedingly

well. In S. cerevisiae, entropic pulling was implemented successfully

to track chaperone interactions during mitochondria translocation

and to assess nascent proteins and aggregates [41]. Our model that

incorporates this synergy represents a progress towards a

mechanistic understanding of chaperone interactions.

Protein aggregation was modeled as a separate module to

monitor protein fate during simulations. Results indicated that

most unfolded and aggregated proteins carried out a transient

interaction with chaperone molecules. Despite the stochastic

binding events between BiP and unfolded proteins, the sequestra-

tion of aggregates can entrap chaperone molecules leading to

decreased chaperone levels. The comparison of BiP-protein

interactions, in terms of folding efficiency and levels of chaperone

cost, was quantified for models containing divergent numbers of

binding sites. Our results indicate that for a given concentration of

BiP and proteins (i.e., nascent, unfolded, or misfolded), single

binding site models provided the highest degree of BiP coverage.

However, experimental evidence previously showed that multiple

chaperone molecules can work in concert to increase protein

refolding and remove aggregates in vivo. Furthermore, our model

revealed that the BiP-protein interaction provides additional

advantages, such that multiple bound BiP molecules prevent

misfolding of U.

Given the parameter uncertainty, we conducted a study that

varied seven parameters (Figure 12) in order to examine the effects

of folding efficiency in the system. Initially, each parameter was

individually altered, as a global search required many sets and

covered only a fraction of the parameter space. We observed that

some parameters were positively correlated with folding efficiency

and others were negatively correlated. The strongest effect came

Figure 11. Chaperone cost. Comparison of the BiP cost of the four models for both non-cooperative and cooperative scenarios. It is better to havelower chaperone cost so that fewer chaperones are required.doi:10.1371/journal.pcbi.1003675.g011



from the disassociation rate of BiP from unfolded proteins, because

the longer the BiP could stay bound, the greater chance that

folding could occur. Note: this analysis varied one parameter at a

time, while keeping the others constant. Global sensitivity analysis,

where all parameters were varied simultaneously, is found in the

Global Sensitivity Analysis Supplement, Text S2.

Due to the highly conserved features between the model

eukaryote, S. cerevisiae, and mammalian protein-folding machinery,

it is extremely likely that these findings for ER translocation and

protein-folding events will translate to higher eukaryotes including

humans. In fact, mammalian BiP (Grp78) appears to have two

functions in protein translocation: (i) it is involved in the insertion

of nascent proteins into the Sec61 complex or opening of the pore

itself [77,78], and (ii) it binds to the nascent protein that laterally

advances through the channel, in a manner similar to a molecular

ratchet that facilitates translocation [79–81]. Recently, experi-

mental studies of the mammalian homolog of the Sec complex –

co-chaperone Sec63 in yeast – has been shown to recruit BiP to

the translocon (i.e. Sec61) and activates BiP for interaction with its

substrates [82], analogous to the BiP’s recruitment to the

translocon in yeast, as described previously. The function of many

subunits of the Sec complex in mammalian cells has remained

elusive due to limited experimental assessments; however, recent

progress has begun to elucidate translocation efficiency, gating

kinetics and functional profiling, and transport effects of subunits

that comprise the mammalian Sec complex [83–85].

Developing spatially-relevant computational models is important

as in vivo experiments, such as single particle tracking (SPT) and

super-resolution fluorescence imaging techniques used to capture

spatial effects at nanometer resolution, are relatively new technol-

ogies [86,87]. Interestingly, under conditions of cell homeostasis BiP

has been found to distribute heterogeneously throughout the yeast

ER, as depicted by live cell imaging and immunofluorescence

techniques [23]. In a similar manner, we conducted fluorescence

spectroscopy experiments to quantify the extent that BiP gradients

exist within the ER lumen (unpublished data). Under conditions of

ER stress, a greater degree of BiP clustering was observed. The

spatial heterogeneity of BiP is displayed via live cell imaging; in

contrast, the translocation pore composed of Sec61 is distributed

homogenously within the ER membrane (Figure S1, Supporting

Information). Via computationally intensive efforts, and only through

providing cooperative action do the advantages of clustering become

evident, providing a mechanistic context for the observed differences.

In conclusion, the chaperone BiP plays several roles in the ER,

namely translocation, protein folding, ER-associated degradation,

and modulation of the UPR. All of these functions require that BiP

perform multiple tasks to complete the process. In translocation,

the accepted model is that of a Brownian ratchet, in which

multiple BiP molecules bind to nascent proteins to transport them

into the lumen [62,63]. BiP’s attempt to correctly fold aberrant

proteins often takes multiple cycles of binding and release. We

show that multiple binding facilitates aggregate dismantling

through more coverage on the structures’ large surfaces. In

addition, our model suggests that the clustering of BiP molecules

would be beneficial in terms of efficiency and chaperone cost

during protein-folding processes in the ER.

Figure 12. Parameter map. Map of the parameter study indentifies effects of varying 7 parameters with respect to protein folding efficiency.doi:10.1371/journal.pcbi.1003675.g012



Supporting Information

Figure S1 Spatial effects of BiP and Sec61 identified by live-cell

imaging. Fluorescent protein variants (i.e. mCherry and yEmCi-

trine, respectively) were fused in-frame to the C-termini of BiP and

Sec61. These recombinant proteins were expressed simultaneously

in haploid S. cerevisiae cells under the control of their endogenous

promoters, as described previously [23,88]. (A) ER-resident

molecular chaperone, BiP, is localized to the nuclear and

peripheral ER subcompartments. Arrows depict the heterogeneity

of BiP distributed throughout the lumen, specifically within the

nuclear ER. (B) In contrast, Sec61 appears to be homogeneously

localized within the nuclear ER membrane, when assessed in

identical cells. (C) DIC image and scale bar of 5 microns. Image

was acquired by confocal microscopy (Zeiss 780 confocal

microscopy, 1006/NA 1.46).

(TIF)

Text S1 Species and reactions supplement.

(PDF)

Text S2 Global sensitivity analysis supplement.

(PDF)

Author Contributions

Conceived and designed the experiments: MG CY ASR. Performed the

experiments: MG CY. Analyzed the data: MG LP. Wrote the paper: MG

CY ASR LP.

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BiP clustering facilitates protein folding in the endoplasmic reticulum

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